Batteries are a useful source of stored energy that can be incorporated into a number of systems. As batteries age, however, they tend to develop high internal resistance that increases with time. In some cases, the internal resistance in a particular cell can become high enough that high constant current to or from the cell results in nonmonotonic charge or discharge voltage evolution.
By way of example, FIG. 1 depicts the simulated discharge voltage profiles for an electrochemical cell for discharge cycles at various stages of the electrochemical cell life. Voltage profile 10 depicts the voltage of an electrochemical cell as the cell is discharged at a time early in the cell life. The voltage profile 10 includes an initial rapid decrease in voltage to about reference point A followed by substantially constant voltage until about reference point B. After Reference point B, the voltage profile 10 exhibits a relatively steady decrease in voltage through the end of the discharge cycle.
Voltage profile 12 depicts the voltage of an electrochemical cell as the cell is discharged at a time later in cell life than the cell life associated with the voltage profile 10. The discharge cycle depicted by the voltage profile 12 begins at a slightly lower voltage compared to the initial voltage of the voltage profile 10 but also exhibits an initial rapid decrease in voltage to about reference point C followed by a slight increase in voltage until about reference point D. The initial decrease in voltage depicted by the voltage profile 12 is more pronounced than the initial decrease in voltage depicted by the voltage profile 10. The increase in voltage between reference point C and D is also different from the substantially constant voltage between the reference points A and B. The voltage profile 12 at all times, however, is lower than the voltage profile 10.
As the age of the electrochemical cell continues to increase as depicted by the voltage profiles 14 and 16, the pattern established by the voltage profiles 10 and 12 continues, with each successive voltage profile (i) beginning at a lower voltage than the earlier voltage profile, (ii) exhibiting a deeper initial drop in voltage, (iii) exhibiting a more significant increase in voltage after the initial voltage drop, and (iv) remaining below the earlier voltage profiles.
The foregoing pattern continues until the age of the electrochemical cell depicted by the voltage profile 18. The initial voltage of the voltage profile 18 along with the initial drop in voltage is such that the electrochemical cell reaches a minimum voltage at which point the discharge cycle of the electrochemical cell is terminated. In some embodiments, this minimum voltage is detected by a battery system and the electrochemical cell is open circuited to prevent cell reversal.
The successively decreasing initial voltage of the voltage profiles 10-18 is a function of the capacity loss of the electrochemical cell. The initial drop in voltage, along with the ensuing rebound, is a function of the internal resistance (in particular the electrolyte impedance) of the electrochemical cell and is described with reference to FIGS. 2-4.
FIGS. 2-4 depict a voltage profile 30, an internal resistance profile 32, and a temperature profile 34, respectively, of a cell during a discharge cycle with a constant discharge current. The open cell voltage 36 of the electrochemical cell is also depicted in FIG. 2. The difference in voltage between the open cell voltage 36 and the voltage profile 30 corresponds to the voltage drop resulting from the internal resistance of the cell.
The power dissipated by the electrochemical cell due to internal resistance is a significant contributor to the temperature of the cell. The rate of the temperature increase of the cell is thus a function of the power dissipated by the electrochemical cell and the power dissipation is a product of the current and the voltage drop resulting from the internal resistance of the cell. Since the current in the discharge cycle of FIGS. 2-4 is being maintained constant, the voltage difference between the open cell voltage 36 and the voltage profile 30 is the primary reason for changes in the rate of temperature increase. Thus, the slope of the temperature profile 34 which is depicted in FIG. 2 by a slope profile 42 tracks with the difference between the open cell voltage 36 and the voltage profile 30.
FIGS. 2-4 thus show that as operation of an electrochemical cell is initiated, the discharge voltage of the electrochemical cell instantaneously drops from the open cell potential 36 to the discharge voltage profile 30 with the amount of voltage drop a function of the internal resistance of the cell. As the electrochemical cell is discharged, FIG. 4 shows that the temperature of the cell increases as indicated by the temperature profile 34. Additionally, the internal resistance of the electrochemical cell increases rapidly as indicated by the internal resistance profile 32 of FIG. 3.
The increasing internal resistance drives the discharge voltage downward toward a minimum discharge voltage 38. The minimum discharge voltage 38 of the voltage profile 30 corresponds with the maximum internal resistance 40 of the internal resistance profile 32.
Once the temperature of the cell increases above a threshold temperature 44 of the temperature profile 34, the internal resistance of the electrochemical cell begins to decrease (see internal resistance profile 32 to the right of point 40 in FIG. 3). The reduced internal resistance is manifested as an increased voltage as shown by the voltage profile 30. The increased voltage profile 30 reduces the difference between the voltage profile 30 and the open cell voltage 36 thereby reducing the rate at which the temperature of the cell is increasing. The increased voltage displayed by the discharge voltage profile 30 indicates that the cell voltage is nonmonotonic.
So long as the minimum discharge voltage 38 of a particular cell is sufficiently high, substantially all of the capacity of the electrochemical cell can be discharged even with a nonmonotonic discharge profile. As the cell ages, however, the minimum discharge voltage 38 becomes lower (see, e.g., voltage profiles 12, 14, and 16 of FIG. 1). Thus, if the electrochemical cell has a minimum allowed discharge voltage 46 (see FIG. 2), then when the discharge voltage reaches the minimum allowed discharge voltage 46 at point 48, discharge of the electrochemical cell is terminated. Thus, all of the capacity to the right of the point 48 of FIG. 2 and under the voltage profile 30, even though stored within the cell, cannot be used.
What is needed therefore is a battery system and method that provides increased access to electrochemical cell capacity.